Abstract
We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of \(\mathfrak {sl}(m, n, D)\) when \(m+n \ge 3\) and D is a superdialgebra, solving, in particular, the problem when D is an associative algebra, superalgebra, or dialgebra. To accomplish this task, we use a different method than the standard studied in the literature. We introduce and use the non-abelian tensor square of Leibniz superalgebras and its relations with the universal central extension.
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The authors were supported by the Ministerio de Economía y Competitividad (Spain), Grants MTM2013-43687-P and MTM2016-79661-P (European FEDER support included) and by Xunta de Galicia, Grant GRC2013-045 (European FEDER support included). X. García-Martínez was also supported by FPU scholarship, Ministerio de Educación, Cultura y Deporte (Spain) and a Fundación Barrié scholarship.
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García-Martínez, X., Ladra, M. Universal Central Extensions of Leibniz Superalgebras Over Superdialgebras. Mediterr. J. Math. 14, 73 (2017). https://doi.org/10.1007/s00009-017-0842-9
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DOI: https://doi.org/10.1007/s00009-017-0842-9